Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.     

Exact results in QED

We consider several applications of the simplest nonlinear QED phenomena described by the light-by-light (LBL) scattering tensor. Among the relevant processes we present the splitting of high energy photon in a Coulomb field, calculate the asymptotics of differential photon photon elastic scattering. We show that LBL mechanism of the four photon mode of neutral pion decay have a dominant role compared, for instance, with the quark loop Feynman amplitude contribution. The mechanisms of creation of two and three gluon jets at colliding electro-positron beams is analyzed. We calculate also the contribution of LBL mechanism to the ortho-positronium decay width. One Of the important application is the analytic calculation of the QED contribution to the anomalous magnetic moment of the muon arising from LBL mechanism realized through electron positron loops, which is enhanced by the logarithm of the ratio of muon to electron masses. The modification of the QED kernel, which takes into account the QED polarization operator is used to extract the pure strong interaction contribution. We consider as well the problem of the Coulomb law modification. At second part of review we consider Moeller scattering process and RC to it. We show that RC are in agreement with renormalization group approach and could be taken into account in form of Drell-Yan process cross-section.     

Some QED processes: Light-by-light and moeller scattering

We consider several applications of the simplest nonlinear QED phenomena described by the light-by-light (LBL) scattering tensor. Among the relevant processes we present the splitting of high energy photon in a Coulomb field, calculate the asymptotics of differential photon photon elastic scattering. We show that LBL mechanism of the four photon mode of neutral pion decay have a dominant role compared, for instance, with the quark loop Feynman amplitude contribution. The mechanisms of creation of two and three gluon jets at colliding electro-positron beams is analyzed. We calculate also the contribution of LBL mechanism to the ortho-positronium decay width. One Of the important application is the analytic calculation of the QED contribution to the anomalous magnetic moment of the muon arising from LBL mechanism realized through electron positron loops, which is enhanced by the logarithm of the ratio of muon to electron masses. The modification of the QED kernel, which takes into account the QED polarization operator is used to extract the pure strong interaction contribution. We consider as well the problem of the Coulomb law modification. At second part of review we consider Moeller scattering process and RC to it. We show that RC are in agreement with renormalization group approach and could be taken into account in form of Drell-Yan process cross-section.     

Gauge-Independence and the Two-Body Problem in QED

I describe a gauge-independent approach to the relativistic two-body bound state and scattering problems in quantum field theory. The basic tool is an ordinary three-dimensional equation involving a potential operator V which gets contributions from both irreducible and reducible diagrams. In QED the resultant V is independent of the choice of covariant gauge used for the photon propagator, unlike the kernel in the Bethe–Salpeter equation. As an illustration, a problem concerning spin-independent level shifts in two-body bound states is analyzed.     

The Barbieri-Remiddi Solution of the Bound-State Problem in QED

We derive the so-called Barbieri-Remiddi solution of the Bethe-Salpeter equation in QED in its general form and discuss its application to the bound-state energy spectrum.     

Running coupling corrections to non-linear evolution for diffractive dissociation

We determine running coupling corrections to the kernel of the non-linear evolution equation for the cross section of single diffractive dissociation in high energy DIS. The running coupling kernel for diffractive evolution is found to be exactly the same as the kernel of the rcBK evolution equation.     

Quantum-electrodynamical photon splitting in magnetized nonlinear pair plasmas

We present for the first time the nonlinear dynamics of quantum electrodynamic (QED) photon splitting in a strongly magnetized electron-positron (pair) plasma. By using a QED corrected Maxwell equation, we derive a set of equations that exhibit nonlinear couplings between electromagnetic (EM) waves due to nonlinear plasma currents and QED polarization and magnetization effects. Numerical analyses of our coupled nonlinear EM wave equations reveal the possibility of a more efficient decay channel, as well as new features of energy exchange among the three EM modes that are nonlinearly interacting in magnetized pair plasmas. Possible applications of our investigation to astrophysical settings, such as magnetars, are pointed out.     

Scalar QED,NLO and PHOTOS Monte Carlo

Recently, QED bremsstrahlung in B meson decays into pair of scalars (πs and/or Ks) has become of interest. If experimental acceptance must be taken into account, the PHOTOS Monte Carlo technique is often used in experimental simulations. We will use scalar QED to benchmark PHOTOS, even though this theory is of limited use for complex objects. We present the analytical form of the kernel used in the older versions of PHOTOS, and the new, exact (scalar QED) one. Matrix element and phase-space Jacobians are separated in the final weight, and future extensions based on measurable electromagnetic form-factors are thus possible. The massive phase-space is controlled in the program with no approximations. Thanks to the iterative solution, all leading and next to leading logarithmic terms are properly reproduced by the Monte Carlo simulation. Simultaneously, full differential distributions over the complete multiple-body phase-space are provided. An agreement of better than 0.01% with independent calculations of scalar QED is demonstrated. PACS 13.20.He; 13.40.Ks     

超强激光驱动的辐射反作用力效应与极化粒子加速

光强超过10~(22) W/cm~2的极端超强激光将光与物质的相互作用推进到辐射主导区域,激发高能伽马光子辐射,产生明显的辐射反作用力效应.辐射反作用力可以显著影响强场中带电粒子的动力学行为,并从根本上改变了极端强场区域的激光等离子体相互作用规律.如何理解和验证辐射反作用力效应是强场物理研究的核心内容之一.本文结合该方向的国内外研究进展,论述了辐射反作用力的经典形式与强场量子电动力学的理论计算与模拟方法,详细讨论了单粒子在强场中的反射、量子随机辐射、自旋-辐射耦合等效应,介绍了激光等离子体相互作用中的电子冷却、辐射俘获、高效伽马辐射等机制,并给出了目前辐射反作用力效应的实验验证方法与进展.针对自旋在强场量子电动力学方面的效应,介绍了激光加速产生极化粒子源的方法.     

The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Functional integral equation for the complete effective action in quantum field theory

Based on a methodological analysis of the effective action approach, certain conceptual foundations of quantum field theory are reconsidered to establish a quest for an equation for the effective action. Relying on the functional integral formulation of Lagrangian quantum field theory, we propose a functional integral equation for the complete effective action which can be understood as a certain fixed-point condition. This is motivated by a critical attitude toward the distinction, artificial from an experimental point of view, between classical and effective action. While for free field theories nothing new is accomplished, for interacting theories the concept differs from the established paradigm. The analysis of this new concept concentrates on gauge field theories, treating QED as the prototype model. An approximative approach to the functional integral equation for the complete effective action of QED is exploited to obtain certain nonperturbative information about the quadratic kernels of the action. As a particular application the approximate calculation of the QED coupling constant α is explicitly studied. It is understood as one of the characteristics of a fixed point given as a solution of the functional integral equation proposed. Finally, within the present approach the vacuum energy problem is considered, as are possible implications for the concept of induced gravity.     

QED in Krein Space Quantization

In this paper we consider the QED in Krein space quantization. We show that the theory is automatically regularized. The three primitive divergences integrals in usual QED are considered in Krein QED. The photon self energy, electron self energy and vertex function are calculated in this formalism. We show that these quantities are finite. The infrared and ultraviolet divergencies do not appear. We discuss that Krein space quantization is similar to Pauli-Villars regularization, so we have called it the “Krein regularization”.     

Can MBPT and QED be merged in a systematic way?

The possiblities of merging QED with the standard many-body perturbation theory (MBPT) for atomic systems in a rigorous and systematic way are analysed. Time-dependent MBPT, based on the time-evolution operator, a technique well developed particularly in nuclear theory, is used and somewhat reformulated to be consistent with the covariant QED formalism. An effective QED Hamiltonian, free from singularities, is constructed. The procedure can be applied to degenerate and quasi-degenerate systems (extended model space), which is not possible with the standard QED technique based upon the S-matrix formulation. To include in the model space closely lying energy levels, such as fine-structure levels, can have a dramatic effect on the convergence rate. The electron-electron interaction is investigated in detail, and it is shown that it can be separated into irreducible multi-photon interactions, which in principle can be iterated as in standard MBPT. Singularities do not appear, and a simple procedure for evaluating residual finite contributions is described. Comparison is made with the closely related Green's function technique. The procedure is presently being tested on the fine-structure levels of He-like ions.     

Ground-state energy of uranium diatomic quasimolecules with one and two electrons

Ground-state energies of the one- and two-electron uranium dimers are calculated for internuclear distances in the range D=40–1,000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac equation without the partial-wave expansion for the potential of two nuclei. The one-electron one-loop QED contributions (self-energy and vacuum polarization) to the ground-state energy are evaluated using the monopole approximation for the two-center potential. Interelectronic interaction of the first and second order is taken into account for the two-electron quasimolecule. Within the QED approach, one-photon-exchange contribution is calculated in the two-center potential, whereas the two-photon-exchange contribution is treated in the monopole approximation.     

A technique for generating Feynman diagrams

We present a simple technique that allows to generate Feynman diagrams for vector models with interactions of order2n and similar models (Gross-Neveu, Thirring model) using a bootstrap equation that uses only the free field value of the energy as an input. The method allows to find the diagrams to, in principle, arbitrarily high order and applies to both energy and correlation functions. It automatically generates the correct symmetry factor (as a function of the number of components of the field) and the correct sign for any diagram in the case of fermion loops. We briefly discuss the possibility of treating QED as a Thirring model with non-local interaction.     

Hydrogen atom spectrum and the lamb shift in noncommutative QED

We have calculated the energy levels of the hydrogen atom as well as the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity.     

The Breit equation as a zeroth-order approximation for calculation of the bound-state energy

An equation whose kernel is determined by the one-photon exchange between interacting particles is analyzed in the framework of the Bethe-Salpeter formalism. This equation is considered as a zeroth-order approximation in the calculation of the corrections to the energy levels. This is the Breit equation that takes into account additional small terms (with respect to the parameter (Zα)²). A procedure that employs the Brillouin-Wigner perturbation theory and makes it possible to sequentially take into account the corrections to the energy levels is considered.     

Fundamental constants and tests of theory in Rydberg states of hydrogenlike ions

A comparison of precision frequency measurements to quantum electrodynamics (QED) predictions for Rydberg states of hydrogenlike ions can yield information on values of fundamental constants and test theory. With the results of a calculation of a key QED contribution reported here, the uncertainty in the theory of the energy levels is reduced to a level where such a comparison can yield an improved value of the Rydberg constant.     

The van der Waals energy of an atom near a carbon nanotube

Using a unified macroscopic QED formalism, an integral equation for the van der Waals energy of a two-level atomic system near a carbon nanotube is derived. The equation is valid for both strong and weak atom-vacuum field coupling. By solving it numerically, the inapplicability of weak coupling-based van der Waals interaction models in the close vicinity of the nanotube surface is demonstrated. It is also shown that encapsulation of doped atoms into the nanotube is energetically more favorable than their outside adsorption by the nanotube surface.